Abstract
Consider the polynomial Pell's equation X 2 - DY 2 = 1, where D = A 2 + 2C is a monic polynomial in Z[x] and deg C < degA. Then for A,C ∈ Q[x], degC < 2, and B = A/C ∈ Q[x], a necessary and sufficient condition for the polynomial Pell's equation to have a nontrivial solution in Z[x] is obtained.
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